HANDOUT 9 Flashcards
(36 cards)
If Y2i is NOT non-stochastic do we have an issue?
YES - this means Y2i is endogenous
Variables that determine attendance
Attend = f(quality, time, location, past-performance) + €2i
Where €2i = motivation, interest, ability = unobservables
What variables determine €1i
€1i = random luck + same unobservables
COV(€1i, €2i)
> 0
higher ability = higher performance
higher ability = higher attendance
COV(attend, €2i)
> 0 by definition
Therefore, COV(attend, €1i)
≠ 0 –> VIOLATES CLRM
Why can’t we use OLS when we have an endogenous variable?
As E(€1i I endogenous variable) ≠ 0 Therefore OLS is BIASED
Implication for OLS estimate of coefficient on attend
As COV(€1i, €2i) > 0 –> UPWARD BIAS
- OLS will overestimate the coefficient on attend
- We get a very positive significant coefficient on attend
- attend could actually have no effect on performance, but appears to have on driven by unobservables
IF COV(€1i, €2i) < 0, OLS –>
DOWNWARD BIAS
Solution to endogeneity
= IV estimation
Two stage least squares
What does IV estimation try to do?
We want a variable that looks like attendance, but it unrelated to €1i.
Replace attend by variables that determine attend but are unrelated to €1i.
2 components of attendance
- systematic - could be instruments
2. random = €2i = get rid of
two stages of IV
- regress attend on instruments that are relevant and exogenous & save fitted values
- Replace attend by attend^ in original regression equation
Is IV unbiased?
NO - but it is CONSISTENT
As n–>infinity, E(b3)–>B3
How can TIME of seminars be a valid instrument for attendance?
If time of seminars is randomly allocated by tabula = unrelated to motivation, interest and ability.
So include 1. Mon/Fri dummy and 2. 9am dummy
Why do we include the original exogenous variables female and a-level when we regress attend on its instruments?
We want the coefficient on attend hat to explain variation in perf over and above females and a-levels “holding all else constant”. If we didn’t include them, maybe the instruments are related to females and a-levels.
2 conditions for IV instruments
- Instrument relevance
2. Instrument exogeneity
What’s the issue if our instruments are only weakly correlated with the endogenous regressor?
Weak correlation –> IV coefficients inconsistent–> t-stats unreliable
Test statistic for weak instruments
B^IV = B + (B^OLS - B)/F
What is F in the test statistic for weak instruments?
F = f-stat from test of joint significance of the coefficients on the instruments when we regress the endogenous regressor on those instruments (+ exogenous variables)
H0: d3 = d4 =0
H1: d3/3 ≠ 0
Rule of thumb for F in the test statistic for weak instruments
F < 10 –> weak instruments
If F=1 in the test statistic for weak instruments
F=1 –> bias of order 100%
We are back to the biased OLS estimate
So IV estimation does NOT help - coefficients are inconsistent.
As F–>infinity in the test statistic for weak instruments
F--> infinity Instruments very significant Bias --> 0 B^IV --> B true coefficient So IV is CONSISTENT.
Instrument exogeneity means
E(€1i I instruments) = 0 Therefore E(€1i I attend^) = 0
